TABLE OF CONTENTS This appendix gives a systematic approach to providing a program for solving propagation, confinement factor and far-field emission when electromagnetic waves are guided by slab waveguides. Almost arbitrary numbers of layers can be computed with complex refractive indices. Chapter 3 covers slabs with only three layers, where there are many fine texts that can provide back-up material [1, 2]. Here, by examining a five-layer system, the way forward to a semi-automated method for an arbitrary number of layers with complex refractive indices is demonstrated. Multilayer guides are particularly relevant in discussing DFB lasers where the longitudinally periodic profile of the permittivity has lateral variations across the waveguide which can be taken into account by having a series of layers with different patterns of permittivity, giving an average permittivity and an average periodic component which can be calculated using the programs.
The classification of TE was given in Appendix 1, where TE plane waves had an H z component because the associated set of orthogonal E, H and ? vectors has ? at a slight angle to the actual O z as in Figure A1.1. This plane wave then 'slaloms' between the slabs with ? z common to all layers but with varying vertical 'propagation' ? y from layer to layer. Five layers of arbitrary material will demonstrate the procedures. Here the top layer is labelled with the symbol T and other layers labelled from 1 to 4...
